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Compute the determinant of \(A^{10}+A\).

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a) Find a \(2 \times 2\) real matrix \(A\) that has an eigenvalue \(\lambda_{1}=1\) with eigenvector \(E_{1}=\) \(\left(\begin{array}{l}1 \\ 2\end{array}\right)\) and an eigenvalue \(\lambda_{2}=-1\) with eigenvector \(E_{2}=\left(\begin{array}{l}2 \\ 1\end{array}\right)\).

b) Compute the determinant of \(A^{10}+A\).
in Mathematics by Platinum (101k points) | 186 views

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